Below is PneumaWord’s outcome of the challenge.
Some of the points have more to do with the person of Jesus, but it is undeniable that His person – including the names He was referred to – are intertwined with His purpose.

Aspects of His purpose unique to a gospel are presented under the books in which they occur, and other aspects that are more common are presented under the book of “John”, because it provides more details about the person and purpose of the Lord Jesus Christ, compared to the other Gospels. Two truths that stand out about Jesus are that “JESUS IS THE CHRIST – THE SON OF GOD” & “JESUS GIVES LIFE – ETERNAL LIFE – TO AS MANY AS WOULD BELIEVE HIM”. The humanity and divinity of Jesus are therefore clearly revealed, as would be seen.

Happy exploring Jesus 🙂

MATTHEW

Jesus came to earth so that God would dwell with us, because He Himself is God, so He dwelling with us means God is with us – Emmanuel (Matthew 1:23).

He came to fulfil the law, not to destroy it (Matthew 5:17).

He came to put a sword in the earth, not peace (Matthew 10:34-35; Luke 12:51).
This doesn’t mean that Jesus delights in violence, but He was just making it clear that allegiance with Him would result in some conflict, because there are those who would not accept His person, even within a family. However, everyone who believes in Jesus experiences peace with God (Romans 5:1) and the peace of God in him/her (Philippians 4:7). That individual can therefore extend peace towards others that are being hostile. It doesn’t mean they would accept it however.

MARK

Jesus is the Holy One of God (Mark 1:24; Luke 4:34).

Jesus is the Son of Man (showing His humanity) with power on earth to forgive sins (Mark 2:10).
Note “on earth”. Beyond earth, there is no forgiveness of sins. That’s why all humans have to repent and acknowledge the person of Jesus as Lord and Saviour, for the remission and forgiveness of sins and for salvation. There is a heaven to gain, which good works can’t take you there, but the righteousness of Christ available to you by faith; and there is a hell to shun. Choose Jesus!
(Mark 8:31; 9:31; 10:33, 45; 14:21; Luke 9:56; 18:31; 19:10: 22:22).

LUKE

Jesus is the Son of the Highest (Luke 1:31-32).

Jesus came to preach the gospel to the poor; heal those whose hearts are broken; preach deliverance to captives; restore sight to blind ones, bring freedom to bruised ones and to proclaim the acceptable year of the Lord (Luke 4:18-19).
The term ‘poor’ used here is not restricted to a state of wealth. Rich people in terms of physical wealth still need salvation if they aren’t born again. Mark 16:15 makes this clear.
Everyone without a relationship with the Lord Jesus Christ is poor spiritually and needs the Gospel (good news) made known to them.
All kinds of a broken heart can be healed by Jesus 🙂
Jesus not only heals those physically blind, but can bring healing to the spiritually blind i.e. those who do not recognise the truth, which is Jesus (2 Cor 4:4; John 14:16).
Many are held captive by addictions, fear etc. Jesus delivers such too! He alone offers true freedom (John 8:36).
The Amplified version of the bible defines the acceptable year of the Lord as “the day when salvation and the free favours of God profusely abound” (Luke 4:18 AMP) and guess what, its now! Jesus made it so!

Jesus came to preach (proclaim and make known) the kingdom of God (Luke 4:43).

Jesus came to call sinners to repentance (Luke 5:32). All who have been born into this world have a sinful nature by default (Rom 3:23; 5:12).

Jesus came as a great prophet, who showed the visitation of God with His people (Luke 7:16).

Jesus came to send fire on the earth (Luke 12:49).

Jesus came to seek and save the lost (Luke 19:10).

He did no wrong (Luke 23:41).

JOHN

Jesus came to empower people to become the sons of God and be born of God (John 1:11-13).

He came to give grace and truth, because He was and still is full of grace and truth (John 1:14,17).

He came to declare i.e. make known the person of the Father to the world (John 1:18). As the Amplified version puts it “He has revealed Him and brought Him out where He can be seen; He has interpreted Him and has made Him known.”

He came to take away the sin of the world (John 1:29).

He came to baptize with the Holy Ghost (Matthew 3:11, Mark 1:7-8; Luke 3:16; John 1:33).

Jesus came to teach the Word of God, as a teacher sent from God (Mark 12:14; John 3:2).

Jesus was a gift given by the Father God to the world. He came to give everlasting and abundant life to whoever would believe in Him (John 3:15-16,36; 4:14; 5:24,26; 6:33-35,44,51,68; 10:10,28; 11:25; 20:31).

Jesus came not to condemn the world but to provide salvation to the world (John 3:17-18).

Jesus came from heaven to speak the Words of God (John 3:31-34).

Jesus came as the Messiah, to “tell all things” (John 4:25-26). This just means that things hidden or unknown of God would and have been made plain and known by Jesus.

Jesus was sent to do the will of Father God and finish His work (John 4:34; 5:19,30,36,43; 8:26; 9:4; 10:25,37-38; 13:3; 17:2-3; 18:11).

Jesus is the bearer of judgement and would judge the world (Matthew 3:12; 12:18-20; Luke 3:17; John 5:22,27-29; 9:39).

Jesus came and was the light of the world, and offers the light of life to whoever would follow Him (Matthew 4:16; Luke 2:32; John 8:12; 9:5).

Jesus came as the Good Shepherd – a living model of how God desires we should live our lives. A shepherd feeds, guides and guards His flock and that is what Jesus does to his sheep – His followers (John 10:11, 14).

Jesus came to die (to be killed,) not only for the salvation of the Jews, but all indeed in the world, so He can gather in one (Himself) children of God scattered about the earth. After dying, He was raised to life on the third day (Matthew 1:21; 12:21, 40; 27:50; Mark 9:31; 10:33-34, 45; 15:31-32; Luke 2:30,34-35; 9:31, 56; 18:33, 24:7; John 11:51-52; 18:31).

Jesus came to be the King of the Jews; King of Israel (Matthew 2:2,6; Mark 11:9-10: Luke 1:31-33; 23:3; John 1:49; 12:13-16; 18:27). Not the literal, physical Israel because His kingdom is not earthly (John 18:36).

Jesus came to make disciples that He further sends into the world, just as He was sent (Matthew 28:18-20; Luke 24:49; John 17:18).

Jesus came to fulfil all that was written about Him in the scriptures (Matthew 2:15,23; 13:34-35; 27:35; Mark 14:21; 15:28; Luke 18:31-33; 22:22; 24:25-26, 44-47; John 16:14; 18:32; 19:28).

Hope you’ve enjoyed finding out the purpose of Jesus. Please feel free to add more on the comments, as you discover them. We are all learning.
God bless you 🙂